# -*- coding: utf-8 -*-
# mathtoolspy
# -----------
# A fast, efficient Python library for mathematically operations, like
# integration, solver, distributions and other useful functions.
#
# Author: sonntagsgesicht, based on a fork of Deutsche Postbank [pbrisk]
# Version: 0.3, copyright Wednesday, 18 September 2019
# Website: https://github.com/sonntagsgesicht/mathtoolspy
# License: Apache License 2.0 (see LICENSE file)
from math import exp
from mathtoolspy.utils.mathconst import ONE_OVER_SQRT_OF_TWO_PI
[docs]def density_normal_dist(x):
""" Density function for normal distribution
@param x: float value
@return value of normal density function
"""
return ONE_OVER_SQRT_OF_TWO_PI * exp(-0.5 * x * x)
[docs]def normal_density(x):
density_normal_dist(x)
[docs]def cdf_abramowitz_stegun(x):
"""
The cumulative distribution function of the standard normal distribution.
The standard implementation, following Abramowitz/Stegun, (26.2.17).
"""
if x >= 0:
# if x > 7.0:
# return 1 - ONE_OVER_SQRT_OF_TWO_PI * exp(-0.5*x*x)/sqrt(1.0+x*x)
result = 1.0 / (1.0 + 0.2316419 * x)
ret = 1.0 - ONE_OVER_SQRT_OF_TWO_PI * exp(-0.5 * x * x) * (
result * (0.31938153 +
result * (-0.356563782 +
result * (1.781477937 +
result * (-1.821255978 +
result * 1.330274429)))))
return ret
if x <= 0:
# if x < -7.0:
# return 1 - one_over_sqrt_of_two_pi() * exp(-0.5*x*x)/sqrt(1.0+x*x)
result = 1.0 / (1.0 - 0.2316419 * x)
ret = ONE_OVER_SQRT_OF_TWO_PI * exp(-0.5 * x * x) * (
result * (0.31938153 +
result * (-0.356563782 +
result * (1.781477937 +
result * (-1.821255978 +
result * 1.330274429)))))
return ret
[docs]def normal_cdf(x):
return cdf_abramowitz_stegun(x)